I posted this question before but had the hypothesis wrong.
here is the correct version. my apologies

f is holomorphic in an open set containing unit disc except for pole at z0
If the power series expansion for f is $\displaystyle \sum_{n=0}^{\infty}\ a_n z^n$
in the open unit disc, then $\displaystyle \lim_{n\to\infty} \frac{a_n}{a_{n+1}} = z_0$

Once again any hints would be greatly appreciated.